Granular and multiphase flows are encountered in a number of industrial processes with particular emphasis in this manuscript given to the particular applications in cement pumping, pneumatic conveying, fluid catalytic cracking, CO2 capture, and fast pyrolysis of bio-materials. These processes are often modeled using averaged equations that may be simulated using computational fluid dynamics. Closure models are then required that describe the average forces that arise from both interparticle interactions, e.g. shear stress, and interphase interactions, such as mean drag. One of the biggest hurdles to this approach is the emergence of non-trivial spatio-temporal structures in the particulate phase, which can significantly modify the qualitative behavior of these forces and the resultant flow phenomenology. For example, the formation of large clusters in cohesive granular flows is responsible for a transition from solid-like to fluid-like rheology. Another example is found in gas-solid systems, where clustering at small scales is observed to significantly lower in the observed drag. Moreover, there remains the possibility that structure formation may occur at all scales, leading to a lack of scale separation required for traditional averaging approaches. In this context, several modeling problems are treated 1) first-principles based modeling of the rheology of cement slurries, 2) modeling the mean solid-solid drag experienced by polydisperse particles undergoing segregation, and 3) modeling clustering in homogeneous gas-solid flows. The first and third components are described in greater detail.

In the study on the rheology of cements, several sub-problems are introduced, which systematically increase in the number and complexity of interparticle interactions. These interparticle interactions include inelasticity, friction, cohesion, and fluid interactions. In the first study, the interactions between cohesive inelastic particles was fully characterized for the first time. Next, kinetic theory was used to predict the cooling of a gas of such particles. DEM was then used to validate this approach. A study on the rheology of dry cohesive granules with and without friction was then carried out, where the physics of different flow phenomenology was exhaustively explored. Lastly, homogeneous cement slurry simulations were carried out, and compared with vane-rheometer experiments. Qualitative agreement between simulation and experiment were observed.

Lastly, the physics of clustering in homogeneous gas-solid flows is explored in the hopes of gaining a mechanistic explanation of how particle-fluid interactions lead to clustering. Exact equations are derived, detailing the evolution of the two particle density, which may be closed using high-fidelity particle-resolved direct numerical simulation. Two canonical gas-solid flows are then addressed, the homogeneously cooling gas-solid flow (HCGSF) and sedimenting gas-solid flow (SGSF). A mechanism responsible for clustering in the HCGSF is identified. Clustering of plane-wave like structures is observed in the SGSF, and the exact terms are quantified. A method for modeling the dynamics of clustering in these systems is proposed, which may aid in the prediction of clustering and other correlation length-scales useful for less expensive computations.